where \(M\)  is the atomic mass, \(\textbf {F}_{tr}\)  is the trapping force, \(\textbf {F}_{rs}\)  is the rescattering force, and \(D\)  is the momentum diffusion coefficient; the effects depend implicitly on time as well as on the MOT parameters mentioned earlier—\(N\) , \(\delta \) , \(\nabla B\) , \(I\) . The dependence on \(N\)  arises from their dependence on \(I\)  that contains information on the cloud density (for \(\textbf {F}_{rs}\) , each particle also contributes to greater repulsion), whereas the dependencies on \(\delta \)  and \(\nabla B\)  arise as these are crucial for a proper description of cooling and confining processes. Finding direct numerical solutions to this equation can be deemed impractical considering both local and nonlocal spatial dependencies. Thus, a more sensible yet an equivalent way of solving the system's dynamics is used by implementing a numerical produce based on a superparticle [1]}, [2]} treatment. As an important remark, note that the Vlasov equation is known to contain NESS solutions [3]}, [4]}, meaning a MOT can potentially be found in such a state. In Section [sec:3]III, we argue that a MOT indeed contains a NESS.
